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184_notes:examples:week2_electric_potential_negative_point [2017/08/25 20:38] – tallpaul | 184_notes:examples:week2_electric_potential_negative_point [2018/05/17 16:49] (current) – curdemma |
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===== Example: Electric Potential from a Negative Point Charge ===== | [[184_notes:pc_potential|Return to Electric Potential]] |
Suppose we have a negative point charge with charge $-Q.WhatistheelectricpotentialatapointP,whichisadistanceR$ from the point charge? | ===== Example: Electric Potential from a Negatively Charged Balloon ===== |
{{ 184_notes:2_potential_negative_point.png?150 |Negative Point Charge -Q, and Point P}} | Suppose we have a negatively charged balloon with total charge $Q=-5.0\cdot 10^{-9} \text{ C}$. What is the electric potential (also called voltage) at a point P, which is a distance $R=20 \text{ m}$ from the center of the balloon? |
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===Facts=== | ===Facts=== |
* The charge with value $-Q$ is a point charge. | * The balloon has total charge $Q=-5.0\cdot 10^{-9} \text{ C}$. |
* The point P is a distance R away from the point charge. | * The point P is a distance $R=20 \text{ m}$ away from the center of the balloon. |
| * The electric potential due to a point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where q represents the charge and r is the distance. |
===Lacking=== | |
* The electric potential at P. | |
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===Approximations & Assumptions=== | |
* The electric potential at P is due entirely to the point charge. | |
* The electric potential infinitely far away from the point charge is $0 \text{ V}$. | |
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===Representations=== | ===Representations=== |
* The electric potential from the point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where $q$ represents our charge ($-Q)andrisourdistance(R$). | <WRAP TIP> |
| === Assumption === |
| We assume P lies outside of the balloon. This is obvious, as $P$ is a distance $R=20 \text{ m}$ away from the center of the balloon. |
| </WRAP> |
| [{{ 184_notes:2_potential_positive_balloon.png?150 |Charged Balloon, and Point P}}] |
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| ===Goal=== |
| * Find the electric potential at $P$. |
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====Solution==== | ====Solution==== |
| <WRAP TIP> |
| === Approximation === |
| We approximate the balloon as a point charge. We do this because we have the tools to find the electric potential from a point charge. This seems like a reasonable approximation because the balloon is not too spread out, and we are interested in a point very far from the balloon, so the balloon would "look" like a point charge from the perspective of an observation location that is 20 m away. |
| </WRAP> |
| |
| <WRAP TIP> |
| === Assumption === |
| The electric potential infinitely far away from the balloon is 0 V. Read [[184_notes:superposition#Superposition_of_Electric_Potential|here]] for why this is important. |
| </WRAP> |
| |
The electric potential at P is given by | The electric potential at P is given by |
\begin{align*} | \begin{align*} |
V &= \frac{1}{4\pi\epsilon_0}\frac{q}{r} \\ | V &= \frac{1}{4\pi\epsilon_0}\frac{q}{r} \\ |
&= \frac{1}{4\pi\epsilon_0}\frac{(-Q)}{R} \\ | &= \frac{1}{4\pi\cdot 8.85\cdot 10^{-12} \frac{\text{C}}{\text{Vm}}}\frac{-5.0\cdot 10^{-9} \text{ C}}{20 \text{ m}} \\ |
&= -\frac{1}{4\pi\epsilon_0}\frac{Q}{R} | &= -2.2 \text{ V} |
\end{align*} | \end{align*} |
| Notice how the magnitude of charge on the balloon is the same as in the "positively charged balloon" [[184_notes:examples:Week2_electric_potential_positive_point|example]]. The reason the magnitude of the voltage is so much smaller, is because the distance is so much greater. [[184_notes:pc_potential#Potential_vs_Distance_Graphs|The closer you get to a point charge, the higher the magnitude of electric potential]]. |